A "change of basis" is an action performed in linear algebra, whereby a change in fundamental structure yields an entirely new viewpoint. This blog began as a record of a pedagogical change of basis for me, and continues as an ongoing account of my thoughts as I design and direct courses in mathematics at the University of North Carolina, Asheville.

Saturday, September 16, 2006

It's Saturday, and I'm just now fixin' to put together a solution sheet for the latest round of representative problems, as I've taken to calling the recommended textbook exercises for 365.

I've spent the afternoon up until now working on a statement of my teaching philosophy, an exercise which meant several hours of agonizing over the right choice of words. Teaching is something I could easily prattle on and on and on and on and on about for chapter after chapter (surprise, surprise), so a good deal of the difficulty lay in cutting what I had to say down to the requested three pages. I was forced to think about the elements of teaching and learning which mean the most to me.

Hmmm...

I'll think some more about that matter. What's on your mathematical minds right now?

In the meantime, I wanted to put out a reminder for my students in 365: please don't forget that Tuesday night at 6:00 we'll have our second problem session, location TBA. I'll be sure to bring a loaf of my homemade apple bread (mmmmmm! apple bread...), and I've already heard murmurred rumors of brownies and soft drinks from some of the students. Please feel free to bring snacks, music, beach balls...whatever will make the session more helpful, more comfortable, more fun. No matter what else you bring, bring yourselves, and let's see if we can break last week's attendance mark of 11!

3 comments:

Anonymous
said...

what's on my mathematical mind right now? i think i'm starting to freak out again over this research paper thing. my group has done absolutely nothing till now! no idea where to start, and i have tons of work and exams in other classes, i'm going crazy. i don't really want to assume leadership of this group either, i'm a perfectionist, and that would be too stressful for me. i have no idea how to go about this. maybe you can address this issue in class and encourage all groups to start working!

Oh no! No freaking out, please! Please? Let me respond with a little advice. Here's the next step (also known as "where to start"): FIND SOME RESOURCES!

You can't write a darned thing until you find out a little something about what you're going to write about, and you can't do that without doing a little reading first.

We'll talk about this more in class tomorrow, but I think a fantastic first step for every team would be (working together, as ideally you have worked on the Scavenger Hunt) to find at least three or four introductory sources and to divvy up the task of beginning to read and understand those. By "divvy up" I don't mean that every person should on her or his own fully read each source singly; that way, no one's going to get the big picture.

A fairer format might be something like:

1. each team finds four sources, say.

2. At the first meeting, each person is assigned one source to skim for general ideas, connections to what we've done in class, et cetera.

3. At the next meeting, each person gives a brief report on the source he or she considered.

4. Based on these reports, and with the sources in front of everyone, piece together a general picture from the sources considered side-by-side. Folks in the team should feel free to trade sources to read more carefully, should they choose to.

5. From here, begin to write down an outline of the context of your research: judging from what you've pieced together from your sources, what is the background of the problem? What are questions that can be asked? Have these questions been answered? If yes, what are those answers? If no, what methods have been tried in order to find answers? Can you understand these methods? Et cetera...each question should naturally flow from the last. Don't force anything, let yourself get used to asking questions: being able to ask good questions is as important as being able to answer them!

6. Repeat these steps as necessary from meeting to meeting, gradually filling in gaps in your understanding by doing your own computations, playing with your own examples, and so forth. Keep a careful record (in research meeting notes that you submit to me, and in your own notes...outline formats work really well for some people, and others like a more "narrative" format) of your work from meeting to meeting, and by the time you need to start writing your progress reports and your final articles, you'll already have a structure for these writing assignments in place.

I hope this helps! Like I said, I'll talk more about this tomorrow and, as you, anonymous, asked, encourage people to get started with that first step this week!

Thanks, by the way, for lighting a fire under my rear. I realize there's a lot going on right now, and it helps me when you all make sure I stay on task and fulfill my end of the bargain.

P.S.: it might be that all it'll take to get your team working is to let them know how you're feeling right now. Maybe saying something like, "hey, folks, I hope we can get underway on this project soon. Why don't we try to meet in the library on [SOME NIGHT] to find some sources?" Chances are everyone else is ready to begin, and wondering where to start, too, and YOU can be the hero!

P.P.S.: I hope it goes without saying (but I'll say it anyway) that I am definitely willing to help your teams out in finding sources should you need the assistance. Some of your topics might be a little harder to find sources on, and some might be really easy. Give it a shot yourselves, and let me know if you run into any problems.

PHEW! yeah, i like that first step you suggested. it makes sense, and it gives me a good place to start. i'm still kinda iffy about this, but i'm really glad your going to address this issue tomorrow in class. maybe our group can meet later on the week to look up sources and divide the work load, assign roles and all.. ah, that would be the greatest relief! i could finally organize my time and see what exactly it is that i have to do regarding this project. thank you!